HMRC have confirmed the K2 scheme is under investigation and have vowed to "challenge it in every way available to them", saying "the Government does not intend anyone, no matter who they are, to get away with paying less than they should."
The tax scheme is understood to protect £168m a year from the taxman in Jersey, with Jimmy Carr as its largest beneficiary.
Speaking at the G20 summit the Prime Minister told ITV News: "I think some of these schemes - and I think particularly of the Jimmy Carr scheme - I have had time to read about and I just think this is completely wrong.
"People work hard, they pay their taxes, they save up to go to one of his shows. They buy the tickets. He is taking the money from those tickets and he, as far as I can see, is putting all of that into some very dodgy tax avoiding schemes.
"That is wrong. There is nothing wrong with people planning their tax affairs to invest in their pension and plan for their retirement - that sort of tax management is fine.
"But some of these schemes we have seen are quite frankly morally wrong.
"The Government is acting by looking at a general anti avoidance law but we do need to make progress on this.
"It is not fair on hard working peole who do the right thing and pay their taxes to see these sorts of scams taking place."
According to a special investigation by the Times newspaper, thousands of high earners in Britain use such schemes to carefully do their accounting “under the radar”.
It claims an accountant disclosed Mr Carr had sheltered £3.3m a year through the company.
Lawyers for the comedian have confirmed he is a member of K2, but categorically denied any wrongdoing, saying the scheme had been disclosed to the relevant authorities in line with the law.
The Government has already announced a crackdown on individual tax avoidance, which is estimated to account for £4.5bn of the £7bn lost in total each year.
He is taking the money from those tickets and he, as far as I can see,
is putting all of that into some very dodgy tax avoiding schemes
David Cameron
Today it was claimed that members of pop group Take That had also invested at least £26m in a scheme believed by HMRC to be a method of avoiding tax.
Singers Gary Barlow, Mark Owen and Howard Donald, along with their manager Jonathan Wild, invested money in a music industry investment scheme used by nearly 1,000 wealthy individuals.
Revenue and Customs officials confirmed it believes the partnerships are designed to allow members to avoid tax and said it will be attempting to close the structure at a tribunal later this year.
Lawyers for Gary Barlow, Mark Owen, Howard Donald and Jonathan Wild confirmed they were investors in two partnerships but told the Times they paid significant tax. There is no suggestion that the scheme is illegal.
Chancellor George Osborne has claimed he was left “shocked” after finding the extent to which multi-millionaires were exploiting tax loopholes and vowed to take “action”.
But shortly after he announced this year’s Budget, the Times alleges the K2 scheme assured its members “most of the powerful tax-saving opportunities survived unscathed.”
It has now published the details of an undercover investigation, in which an accountant promised to cut the tax bill on a £280,000 salary from £127,000 to just £3,500.
Roy Lyness, from Peak Performance Accountants which run the K2 scheme, told a seminar of businessmen: “It’s a game of cat and mouse. The Revenue closes one scheme, we find another way round it.
“It’s like a sat nav. I’m driving to Manchester, get a message saying there’s a smash at Stoke, press the button to re-route. That’s all we do with tax avoidance.”
He added the company did not broadcast the scheme because doing so would be like a “red rag to a bull”.
The scheme works by transferring salaries into a trust based in Jersey, which will then lend investors back the money. The loan, which can technically be recalled, is not subject to income tax.
Mr Lyness told the newspaper full details of the scheme had been providedto HMRC in accordance with regulations.
A spokeswoman for HMRC said: "This scheme (K2) was already under investigation by HMRC. If, as is alleged, it depends on the use of loans it will not work.
"HMRC are looking into this. If the scheme does work technically, HMRC will challenge it in every way available to them.
"Government does not intend anyone, no matter who they are, to get away with paying less than they should."
In April, George Osborne told The Daily Telegraph: “I was shocked to see that some of the very wealthiest people in the country have organised their tax affairs, and to be fair it’s within the tax laws, so that they were regularly paying virtually no income tax. And I don’t think that’s right.
“I’m talking about people right at the top. I’m talking about people with incomes of many millions of pounds a year. The general principle is that people should pay income tax and that includes people with the highest incomes.
“I’m not allowed to be shown the names of the individuals but I’ve sat with the most senior people at the Inland Revenue, the people who run some of the high net worth units there. They have given me examples, anonymised examples, and so we are taking action.”
Today, treasury minister MP David Gauke told the BBC’s World at One he agreed such tax avoidance schemes were “morally repugnant”.
He said: “Where there are arrangements that are artificial, that are contrived, that are not undertaken for genuine commercial reasons but designed to reduce tax liability, that is something we want to address.
“The government is doing an awful lot in this area and we have taken a number of measures to reduce tax avoidance.”
He confirmed “HMRC is already investigating this particular scheme” and suggested the accountant may have been over-selling its effectiveness in order to secure customers.
Seven different schemes have already been closed down in the last year, he said, but admitted “there is more to do”.
“Most people are paying the right amount of tax and it is not right that there is a minority that are getting away with it,” he said.
Jimmy Carr, who performed at the Queen’s Diamond Jubilee celebrations, is a stand up comedian and is currently best known as the host of Channel 4’s 8 out of 10 Cats.
On the show Ten O'Clock Live he performed a sketch lampooning Barclays over its tax arrangements, and referred to "the world's biggest, most aggressive team of blood-hungry amoral tax lawyers."
His management have not responsed to requests for comment.